Question

80 POINTS for right answer! 4 questions! Math only

Question 1 (Multiple Choice Worth 4 points)


(07.05A)

Which of the following has a graph that is a straight line?

Equation 1: y = 5x2 + 41

Equation 2: y = 14x5 − 4

Equation 3: y = 12x + 17

Equation 4: y4 = 2x − 1



Which of the following ordered pairs could be placed in the table and still have the relation qualify as a linear function?



Input
(x)

Output
(y)


−1 4
0 7
1 10
? ?


(2, 7)

(2, 13)

(1, 7)

(−1, 13)


Which statement best explains whether the table represents a linear or nonlinear function?



Input
(x)

Output
(y)


−2 7
−5 4
−8 1
−11 −2


It is a linear function because there is a constant rate of change in both the input and output values.

It is a nonlinear function because there is a constant rate of change in both the input and output values.

It is a linear function because the input values are decreasing.

It is a nonlinear function because the input values are increasing.


Which statement best explains whether y = 3x + 5 is a linear function or a nonlinear function?

It is a linear function because its graph contains the points (0, 0), (1, 0), (2, 8), which are on a straight line.

It is a linear function because its graph contains the points (0, 0), (1, 0), (2, 4), which are not on a straight line.

It is a nonlinear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.

It is a linear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.

Answer 1

Answer:it’s linear and is straight

Explanation:

Answer 2

1.
A graph of linear function is a straight line.
Linear function in a slope-intercept form: y = mx + b

Answer: Equation 3: y = 12x + 17.

2.
x|-1 | 0 | 1 | ? |
y| 4 | 7 |10| ? |

a slope:
`m=(y_2-y_1)/(x_2-x_1)`

We choose:

`(-1; 4)\to x_1=-1\ and\ y_1=4\\(0;\ 7)\to x_2=0\ and\ y_2=7`

subtitute:


`m=(7-4)/(0-(-1))=(3)/(1)=3`

a slope-intercept form:
`y-y_1=m(x-x_1)`

subtitute:


`y-4=3(x-(-1))\\\\y-4=3(x+1)\\\\y-4=3x+3\ \ \ \ |add\ 4\ to\ both\ sides\\\\y=3x+7\ (*)`

subtitute x = 2 to the equation (*):


`y=3\cdot2+7=6+7=13`

Answer: (2, 13)


3.
(-2; 7), (-5; 4)

the slope:
`m=(4-7)/(-5-(-2))=(-3)/(-5+2)=(-3)/(-3)=1`


`y-7=1(x-(-2))\to y-7=x+2\ \ \ \ |add\ 7\ to\ both\ sides\\y=x+9`

check other:


`(-8;\ 1)\to L=1;\ R=-8+9=1;\ L=R-correct\\(-11;-2)\to L=-2;\ R=-11+9=-2;\ L=R-correct`

The conclusion: It's a linear function

Answer: It is a linear function because there is a constant rate of change in both the input and output values.


4.
y = 3x + 5 /look at the picture/

Answer: It is a linear function because its graph contains the points (0, 5), (1, 8), (2, 11), which are on a straight line.

check:

`(0; 5)\to L=5; R=3\cdot0+5=5;\ L=R-correct\\(1;\ 8)\to L=8;\ R=3\cdot1+5=8;\ L=R-correct\\(2;\ 11)\to L=11;\ R=3\cdot2+5=11;\ L=R-correct`